The non-abelian D-brane effective action through order α′4\alpha'{}^4

Requiring the existence of certain BPS solutions to the equations of motion, we determine the bosonic part of the non-abelian D-brane effective action through order $\alpha'{}^4$. We also propose an economic organizational principle for the effective action.Comment: 12 pages, 2 figures, JHEP styl

Supersymmetric sources, integrability and generalized-structure compactifications

In the context of supersymmetric compactifications of type II supergravity to four dimensions, we show that orientifold sources can be compatible with a generalized SU(3) x SU(3)-structure that is neither strictly SU(3) nor static SU(2). We illustrate this with explicit examples, obtained by suitably T-dualizing known solutions on the six-torus. In addition we prove the following integrability statements, valid under certain mild assumptions: (a) for general type II supergravity backgrounds with orientifold and/or D-brane generalized-calibrated sources, the source-corrected Einstein and dilaton equations of motion follow automatically from the supersymmetry equations once the likewise source-corrected form equations of motion and Bianchi identities are imposed; (b) in the special case of supersymmetric compactifications to four-dimensional Minkowski space, the equations of motion of all fields, including the NSNS three-form, follow automatically once the supersymmetry and the Bianchi identities of the forms are imposed. Both (a) and (b) are equally valid whether the sources are smeared or localized. As a byproduct we obtain the calibration form for a space-filling NS5-brane.Comment: 32 pages, 1 table, v2: added references, v3: corrected mistake in (4.1) leading to factor 2 mistake in (B.6), corrected (B.5), smaller typo

From ten to four and back again: how to generalize the geometry

We discuss the four-dimensional N=1 effective approach in the study of warped type II flux compactifications with SU(3)x SU(3)-structure to AdS_4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-perturbative corrections to this superpotential arising from gaugino condensation or Euclidean D-brane instantons. For the latter we derive the supersymmetry conditions in N=1 flux vacua in full generality. We find that the non-perturbative corrections induce a quantum deformation of the internal generalized geometry. Smeared instantons allow to understand KKLT-like AdS vacua from a ten-dimensional point of view. On the other hand, non-smeared instantons in IIB warped Calabi-Yau compactifications 'destabilize' the Calabi-Yau complex structure into a genuine generalized complex one. This deformation gives a geometrical explanation of the non-trivial superpotential for mobile D3-branes induced by the non-perturbative corrections.Comment: LaTeX, 47 pages, v2, references, hyperref added, v3, correcting small inaccuracies in eqs. (2.6a) and (5.16

D-branes on AdS flux compactifications

We study D-branes in N=1 flux compactifications to AdS_4. We derive their supersymmetry conditions and express them in terms of background generalized calibrations. Basically because AdS has a boundary, the analysis of stability is more subtle and qualitatively different from the usual case of Minkowski compactifications. For instance, stable D-branes filling AdS_4 may wrap trivial internal cycles. Our analysis gives a geometric realization of the four-dimensional field theory approach of Freedman and collaborators. Furthermore, the one-to-one correspondence between the supersymmetry conditions of the background and the existence of generalized calibrations for D-branes is clarified and extended to any supersymmetric flux background that admits a time-like Killing vector and for which all fields are time-independent with respect to the associated time. As explicit examples, we discuss supersymmetric D-branes on IIA nearly Kaehler AdS_4 flux compactifications.Comment: 43 pages, 2 pictures, 1 table; v2: added references, color to figure and corrected typo in (6.21b

On moduli and effective theory of N=1 warped flux compactifications

The moduli space of N=1 type II warped compactions to flat space with generic internal fluxes is studied. Using the underlying integrable generalized complex structure that characterizes these vacua, the different deformations are classified by H-twisted generalized cohomologies and identified with chiral and linear multiplets of the effective four-dimensional theory. The Kaehler potential for chiral fields corresponding to classically flat moduli is discussed. As an application of the general results, type IIB warped Calabi-Yau compactifications and other SU(3)-structure subcases are considered in more detail.Comment: 54 pages; v3: comments and references added, version published in JHE

AdS Vacua, Attractor Mechanism and Generalized Geometries

We consider flux vacua attractor equations in type IIA string theory compactified on generalized geometries with orientifold projections. The four-dimensional N=1 superpotential in this compactification can be written as the sum of the Ramond-Ramond superpotential and a term described by (non)geometric flux charges. We exhibit a simple model in which supersymmetric AdS and Minkowski solutions are classified by means of discriminants of the two superpotentials. We further study various configurations without Ramond-Ramond flux charges. In this case we find supersymmetric AdS vacua both in the case of compactifications on generalized geometries with SU(3) x SU(3) structures and on manifolds with an SU(3)-structure without nongeometric flux charges. In the latter case, we have to introduce correction terms into the prepotential in order to realize consistent vacua.Comment: 35 pages, accepted version in JHE

A second look at N=1 supersymmetric AdS_4 vacua of type IIA supergravity

We show that a class of type IIA vacua recently found within the N=4 effective approach corresponds to compactification on Ads_4 \times S^3 \times S^3/Z_2^3. The results obtained using the effective method completely match the general ten-dimensional analysis for the existence of N=1 warped compactifications on Ads_4 \times M_6. In particular, we verify that the internal metric is nearly-Kahler and that for specific values of the parameters the Bianchi identity of the RR 2-form is fulfilled without sources. For another range of parameters, including the massless case, the Bianchi identity is satisfied when D6-branes are introduced. Solving the tadpole cancellation conditions in D=4 we are able to find examples of appropriate sets of branes. In the second part of this paper we describe how an example with internal space CP^3 but with non nearly-Kahler metric fits into the general analysis of flux vacua.Comment: Latex file, 35 pages, no figures. Reference added, minor corrections adde

N=2 solutions of massive type IIA and their Chern-Simons duals

We find explicit AdS4 solutions of massive type IIA with N=2 supersymmetry obtained deforming with a Roman mass the type IIA supersymmetric reduction of the M theory background AdS4 times M111. The family of solutions have SU(3) times SU(3) structure and isometry SU(3) times U(1)^2. They are conjectured to be dual to three-dimensional N=2 Chern-Simons theories with generic Chern-Simons couplings and gauge group ranks.Comment: 20 pages, 1 figure, comments and references adde

D-branes in Generalized Geometry and Dirac-Born-Infeld Action

The purpose of this paper is to formulate the Dirac-Born-Infeld (DBI) action in a framework of generalized geometry and clarify its symmetry. A D-brane is defined as a Dirac structure where scalar fields and gauge field are treated on an equal footing in a static gauge. We derive generalized Lie derivatives corresponding to the diffeomorphism and B-field gauge transformations and show that the DBI action is invariant under non-linearly realized symmetries for all types of diffeomorphisms and B-field gauge transformations. Consequently, we can interpret not only the scalar field but also the gauge field on the D-brane as the generalized Nambu-Goldstone boson.Comment: 32 pages, 4 figures, ver2:typos corrected, references adde

Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications

We consider compactifications of type II string theory on general SU(3) x SU(3) structure backgrounds allowing for a very large set of fluxes, possibly nongeometric ones. We study the effective 4d low energy theory which is a gauged N=2 supergravity, and discuss how its data are obtained from the formalism of the generalized geometry on T+T*. In particular we relate Hitchin's special Kaehler metrics on the spaces of even and odd pure spinors to the metric on the supergravity moduli space of internal metric and B-field fluctuations. We derive the N=1 vacuum conditions from this N=2 effective action, as well as from its N=1 truncation. We prove a direct correspondence between these conditions and an integrated version of the pure spinor equations characterizing the N=1 backgrounds at the ten dimensional level.Comment: 54 pages. v2, v3: minor change